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The influence of noncommutativity on the local stability of the accelerating (un)charged Schwarzschild black hole is what we aim to investigate. It results in the C-metric description of accelerating Schwarzschild black hole. Such a notion describes a pair of separated black holes that accelerate in opposite directions under the action of forces represented by conical singularities. However, the impact of spatial noncommutativity on the thermodynamic properties of an accelerating (un)charged Schwarzschild black hole is explored by analyzing the Gaussian distribution of mass and charge densities, reflecting the smearing effects due to noncommutative geometry. We begin the study with the uncharged case, examining the influence of noncommutativity and acceleration. This approach highlights how these parameters jointly modify the temperature, entropy, and heat capacity of the black hole, deviating from classical thermodynamics. Next, the charged case is considered, introducing additional complexity as charge density now interacts with both noncommutativity and acceleration. This scenario reveals further modifications in the black hole’s thermodynamic behavior. The effects of noncommutativity and acceleration are reexamined, revealing further interactions and modifications of the black hole’s thermodynamic properties. By addressing these two cases sequentially, the paper offers new insights into black holes in noncommutative and accelerated geometries.
Chacha et al. (Fri,) studied this question.